I’ve noticed that many archetypes with a level 2 dedication feat simply don’t have any level 4 feats. How does this work with the free archetype variant rule? Do you just discard the bonus feat slot at level 4? Also, does playing with this variant rule essentially make it impossible to take a level 4 dedication feat at level 4?
No. Feat from free archetype has to be from its dedication and it cannot be skill feat. And unless the GM says otherwise, normally level 4 dedication can’t be taken with free archetype at level 2 or 4 (level 6 is possible since in certain dedication you can get 2 feat in level 4).